Leaders in House and Senate Haven't Joined the Effort, Which Could Trigger a Vote Before Midterms

WASHINGTON—A handful of lawmakers are saying President Barack Obama must get congressional authorization for military action in Iraq, a vote that could exacerbate tensions between the branches and present members with a difficult vote just before the midterm elections.

Mr. Obama's announcement of limited airstrikes last week aimed at slowing the advance of militants from the Islamic State toward the Kurdish city of Erbil initially triggered few complaints that he had usurped the power to declare war that Congress claims as...